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Théorie des noeuds et musique| old_uid | 7953 |
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| title | Théorie des noeuds et musique |
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| start_date | 2010/01/15 |
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| schedule | 14h30-18h30 |
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| online | no |
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| summary | Franck Jedrzejewski (CEA Saclay - INSTN/UESMS) : Classification des groupes sériels
Après un rappel sur la constitution des diagrammes de cordes liés aux séries dodécaphoniques, nous donnons la définition d'un groupe sériel. Nous montrons qu'il existe seulement 26 groupes sériels qui sont des cas particuliers des 301 groupes transitifs des permutations de 12 notes. Nous étudions l'action de ces groupes sur les séries et donnons quelques propriétés. Enfin, nous envisageons l'imprimitivité de ces groupes et explicitons les systèmes blocs qui leur sont associés.
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Leone Slavich (University of Pisa / Ircam) : Classification of n-tone rows with generalized chord diagrams
The notion of chord diagram built from an n-tone row can be generalized by associating notes belonging to cosets of subgroups different from Z/2Z (the traditional case of the tritone). With this machinery, it becomes possible to refine the classification of n-tone rows, by identifying series if and only if they have the same generalized chord diagram, no matter which subgroup it is built with. A mathematical formalization of the whole theory allows this identification to be obtained through the action of a group G on the set of n-tone rows. An explicit description of this group can be obtained with the use of some basic combinatorial algebra. In the end, one obtains a description of G as a chain of semidirect products of easily describable groups.
This allows to show that, in the case of n = 12, it is possible to classify dodecaphonic series up to the set of affine transformations. In the general case however, one obtains a bigger group of transformations.
Références :
[1] F. Jedrzejewski, Mathematical Theory of Music, Collection « Musique/Sciences », Ircam-Delatour France, 2006.
[2] V. Manturov, Knot Theory, CRC, 2004.
[3] W.B.R. Lickorish, An Introduction to Knot Theory, Springer 1997.
[4] John D. Dixon & Brian Mortimer, Permutation Groups, Springer, 1996.
[5] Peter J. Cameron, Permutation Groups, Cambridge University Press, 1999. |
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| oncancel | chgt de date |
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| responsibles | Agon Amado, Andreatta |
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